Stability of the reverse Blaschke-Santaló inequality for zonoids and applications

DOI10.1016/j.aam.2009.09.002zbMath1191.52002OpenAlexW1976102239MaRDI QIDQ962000

Károly jun. Böröczky, Daniel Hug

Publication date: 1 April 2010

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aam.2009.09.002

zbMATH Keywords

zonoidMahler's conjecturestability resultzero cellPoisson hyperplane tessellationvolume productreverse Blaschke-Santaló inequality

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Inequalities and extremum problems involving convexity in convex geometry (52A40) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items

Equipartitions and Mahler volumes of symmetric convex bodies, Second moments related to Poisson hyperplane tessellations, Introduction to Stochastic Geometry, On the stability of the \(p\)-affine isoperimetric inequality, Minimal volume product near Hanner polytopes, Stability of the reverse Blaschke-Santaló inequality for unconditional convex bodies, The planar Busemann-Petty centroid inequality and its stability, Intersection and proximity of processes of flats, LOCAL MINIMALITY OF THE VOLUME‐PRODUCT AT THE SIMPLEX

Cites Work

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• Asymptotic shapes of large cells in random tessellations
• Some functional inverse Santaló inequalities
• Increasing functions and inverse Santaló inequality for unconditional functions
• Duality, volume product and Mahler's inequalities
• From the Mahler conjecture to Gauss linking integrals
• Zonoids with minimal volume-product
• Une caractérisation volumique de certains espaces normés de dimension finie. (A volume characterization of some finite dimensional normed spaces)
• On a reverse form of the Brascamp-Lieb inequality
• Convex bodies with minimal volume product in \(\mathbb{R}^ 2\)
• A special case of Mahler's conjecture
• Contributions to affine surface area
• Blaschke-Santaló inequalities
• \(L_ p\) affine isoperimetric inequalities.
• New volume ratio properties for convex symmetric bodies in \({\mathbb{R}}^ n\)
• The limit shape of the zero cell in a stationary Poisson hyperplane tessellation.
• Mahler's conjecture and wavelets
• Some functional forms of Blaschke-Santaló inequality
• Volume inequalities for subspaces of \(L_p\)
• Convergence of algorithms for reconstructing convex bodies and directional measures
• On the Blaschke-Santaló inequality
• The case of equality for an inverse Santaló functional inequality
• Volume Inequalities forL_p‐Zonotopes
• Shadow Systems and Volumes of Polar Convex Bodies
• Volume Ratios and a Reverse Isoperimetric Inequality
• Stochastic and Integral Geometry
• Borsuk's theorem and the number of facets of centrally symmetric polytopes
• Random polytopes and the volume-product of symmetric convex bodies.
• Minimal Volume-Product in Banach Spaces with a 1-Unconditional Basis
• Zonoids with Minimal Volume-Product--A New Proof
• Random Polytopes Generated by Anisotropic Hyperplanes
• The Brunn-Minkowski inequality
• Real Analysis and Probability
• Extremal Properties of Random Mosaics
• On volume product inequalities for convex sets
• Convex and Discrete Geometry
• Volume inequalities for isotropic measures
• The Santaló point of a function, and a functional form of the Santaló inequality
• Distances of Probability Measures and Random Variables
• A theorem on transfer for convex bodies
• Optimal Transport